Machine Translation (MT) for low-resource languages has been challenging so far, mainly due to the small size or lack of parallel sentences. Parallel sentence mining and filtering are two automatic approaches which aim to identify and curate such resources. Yet, they usually rely on multilingual representation as a backend, which is known to be of poorer quality for low-resource language pairs, leading to the introduction of noisy pairs. We devise SNAPP, a post-processing pipeline which combines a segment-level filtering technique with an unsupervised neural aligner to remove highly similar but non-parallel sentence pairs. Modular components further enable more specific adaptation to the language pair under consideration. We evaluate filtering performance on three language pairs of varying typological distance. Finally, we show improvement on the downstream MT performance with our post-processing pipeline for the two harder language pairs.